However, the numbering system found in one kind of circuit may be dissimilar to that of a different type of circuit, for instance, the memory of a computer would use hexadecimal numbers as the keyboard uses decimal numbers.

**Source: convert text to binary**

Then the conversion in one number system to some other is essential with the four main types of arithmetic being.

- Decimal – The decimal numbering system includes a base of 10 (MOD-10) and uses the digits from 0 through 9 to represent a decimal number value.
- Binary – The binary numbering system includes a base of 2 (MOD-2) and uses only two digits a “0” and a “1” to represent a binary number value.
- Octal – The octal numbering system includes a base of 8 (MOD-8) and uses 8 digits between 0 and 7 to represent an octal number value.
- Hexadecimal – The Hexadecimal numbering system includes a base of 16 (MOD-16) and runs on the total of 16 numeric and alphabetic characters to represent lots value. Hexadecimal numbers contain digits 0 through 9 and letters A to F.

Long binary numbers are difficult to both read or write and tend to be converted into something easier understood or user-friendly. Both most common derivatives predicated on binary numbers will be the Octal and the Hexadecimal numbering systems, with both these limited long to a byte (8-bits) or a word (16-bits).

Octal numbers could be represented by sets of 3-bits and hexadecimal numbers by sets of 4-bits together, with this grouping of the bits being found in electronic or personal computers in displays or printouts. The grouping together of binary numbers could also be used to represent Machine Code used for programming instructions and control such as for example an Assembly Language.

Comparisons between your various Decimal, Binary, Hexadecimal and Octal numbers receive in the next table.

**Digital Numbering System Comparison Table**

Base, b | Byte (8-bits) | Word (16-bits) |

Decimal | 0 to 255 _{10} |
0 to 65,535 _{10} |

Binary | 0000 0000 to 1111 1111 _{2} |
0000 0000 0000 0000 to 1111 1111 1111 1111 _{2} |

Hexadecimal | 00 to FF _{16} |
0000 to FFFF _{16} |

Octal | 000 to 377 _{8} |
000 000 to 177 777 _{8} |

We are able to see from the table above that the Hexadecimal numbering system uses only four digits expressing an individual 16-bit word length, and for that reason it is the mostly used Base Numbering System for digital, micro-electronic and personal computers.